Direct numerical simulation of complex nano-structured composites, considering interface stretching and bending effects, using nano-computational grains

Driven by the promising applications of nano-composites, the Steigmann–Ogden (S-O) interface stress model is used together with the classical Elasticity theory to model the effective mechanical properties of nano-composites, considering both interface stretching and bending effects. However, no literature has been reported on analytical or numerical solutions for composites containing multiple three-dimensional nano-inclusions with S-O interfaces. In order to overcome this difficulty, a new type of computational grain (CG) is developed with an embedded spherical inclusion and S-O matrix/inclusion interface. The stiffness matrix of each CG is computed by a new boundary-type multifield variational principle together with Papkovich–Neuber potentials. By evaluating and assembling stiffness matrices of CGs along with parallel computations, very efficient direct numerical simulations of complex nano-composites with a large number of inclusions in a Representative Volume Element of the nanocomposite are essentially realized. Numerical examples demonstrate the validity and the power of the currently developed CGs. Especially, material models with 10,000 nano-inclusions are simulated in around 50 min on the 16-core workstation. The influence of interface elastic bending parameters and spatial distributions of the nano-inclusions on the overall properties of nano-composites is also investigated in this study.